Virtual manipulatives as cognitive tools, dynamic/interactive, Web-based representations and/or technology-based renditions, allow users to engage in mathematical meaning making. This research investigated teacher candidates' perceptions of the mathematical, cognitive, and pedagogical fidelity of Fill and Pour virtual manipulative. Findings…

Prospective teachers (PTs), enrolled in a mathematics methods course, were asked to analyze children's mathematical thinking by viewing videotaped clinical interviews over the course of an entire semester. They were also asked to conduct two of their own interviews with children as the semester progressed. While the type of analysis varied, all of…

The goal of this study is to better understand preservice elementary teachers' changes in attitudes towards mathematics in connection with their participation in a module aimed at developing professional noticing capacities. This module, typically implemented in the mathematics methods course, involves practice with the three interrelated…

This paper presents the results of a study designed to facilitate teacher candidates' shift from students of mathematics to teachers of mathematics. We develop a series of tasks each of which encourages candidates to reconsider rich tasks from increasingly teacher-centric points of view. The results show that using authentic high school student…

Teacher education programs have increasingly incorporated activities to support novice teachers in learning to attend to student ideas that surface during mathematics instruction. These efforts have been found to be effective at the end of a particular course, but less is known about their longer-term effects on teaching practice. A related study…

This study explores the hypothesis that experience with children's mathematical thinking facilitates the development of teachers' professional knowledge. Multilevel models of a data set representative of US public institutions preparing K-6 teachers from the Teacher Education and Development Survey in Mathematics (Brese & Tatto, 2012)…

As creating and critiquing arguments becomes more of a focus in mathematics classes, teachers need to develop their abilities to facilitate productive arguments. Toulmin's (1958/2003) model of argumentation has been useful in analyzing arguments in mathematics education research, raising the question whether it would assist mathematics teachers as…

These Proceedings are a written record of the research presented at the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2012) held in Kalamazoo, Michigan, November 1-4, 2012. The theme of the conference, "Navigating Transitions along Continuums," focuses on…

The non-normative application of proportional strategies in non-proportional covariance situations is widespread and documented in studies conducted in many countries and with participants across a wide range of ages. In the present study, we found that preservice middle-grades teachers have many of the same problems with proportional reasoning as…

This study questions the extent to which a course in Mathematical Problem Solving with Technology was developing TPACK in mathematics preservice teachers. In order to measure the development of TPACK, both quantitative and qualitative data were collected. Preliminary findings are promising. Preservice teachers developed a vision of technology use…

This study investigates cognitive difficulties and mathematical ideas that are related to making connections among representations. A three-week intervention was designed and implemented to help prospective secondary mathematics teachers develop understanding of big ideas that are critical to connection of representations in algebra. This study…

We present findings from a study of prospective middle school teachers' reasoning as they transitioned from thinking arithmetically to thinking algebraically about even and odd numbers. Teachers were asked to make sense of and use two representations of even and odd numbers to model them and to make connections between the representations.…

This paper describes a synthesis conducted to determine what research says regarding preservice teachers' understanding of fractions and identify the gaps in their existing knowledge basis. Specifically, this paper will address a smaller portion of the synthesis and report the findings from fraction multiplication and division topics. Results…

A critical practice in teaching elementary mathematics is posing problems that build on children's mathematical thinking. As such, teacher educators must provide pre-service teachers (PSTs) with a set of learning experiences to support PSTs in this practice. In this study, we present our analyses of PSTs' responses to a sequence of three methods…

This paper presents partial results of a completed study which investigated the experience of teaching mathematics content courses to preservice elementary teachers. Interviews with ten mathematics instructors who teach these courses revealed several major tensions, including one that arises as instructors strive to set priorities and balance…